Question

Q 8

Answer 1

Let G₁, G₂, G₃, G₄, G₅ be five geometric means between a = 1 and b = 27

Then, 1, G₁, G₂, G₃, G₄, G₅, 27 is a G.P.
Thus, we have
First term = a = 1
7^th term of the G.P. = ar⁶ = 27

⇒ 1 x r⁶ = 27

⇒ r⁶ = 27

⇒ (r²)⁶ = (3)³

⇒ r² = 3

⇒ r = `sqrt3`

∴ G₁ = ar = 1 x `sqrt3 = sqrt3`

 G₂ = ar² = 1 x `(sqrt3)^2` = 3

G₃ = ar³ = 1 x `(sqrt3)^3=3sqrt3`

G₄ = ar⁴ = 1 x `(sqrt3)^4` = 9

G₅ = ar⁵ = 1 x `(sqrt3)^5 = 9sqrt3`